Industry demands new engineering and material solutions. One of these solutions are fibre reinforced polymers. They are light and strong for application as a material for I-beams. An I-beam is the best section for a homogeneous material because of the highest resistance moment. The popularity of composite materials introduces wide use in most branches of engineering and mostly as fibre reinforced polymers (FRP). This paper presents numerical and analytical studies on the mechanical behaviour of the I-beams made of fibre reinforced polymers reinforced by glass fibres (GFRP) and carbon fibres (CFRP) comparing to the structural steel S235JR. Five I-beams with different composite structures and one steel I-beam were numerically tested. Four-point test according to ASTM C 78 – 02 was conducted. Numerical simulation made in SOLIDWORKS software in the Static simulation mode was used. The obtained results were analysed and an attempt to determine the optimal parameters for combination of different composite materials was conducted. As a result of numerical analysis values of deflection and normal stress were obtained for polymer I-beam reinforced by glass and carbon fibres comparing to the steel I-beam.